Exercises for Chapter 3, Decision Analysis

BSNS2120, J. Wang

Name ______________________1. Decision making is for ______________.a. determining what to do next or in the futureb. evaluating what we did in the pastc. Both a and b.2. Making decision is to select a state of nature.a. Trueb. False3. As the result of decision making, ______________.a. one and only one state of nature will be selectedb. more than one state of nature can be selectedc. one and only one decision alternative is selectedd. more than one decision alternative can be selected4. A decision maker does not have much control on _____________.a. selecting a decision alternativeb. states of nature5. When making decision, the decision maker ______ which state of nature will actually occur.a. knowsb. does not know6. The selection of decision alternatives will affect the actual occurrence of the state of nature.a. Trueb. False7. The actual payoff is affected by the selected decision alternative.a. Trueb. False8. The actual payoff is affected by which state of nature will actually occur.a. Trueb. False9. In a decision table, a state of nature is associated with a _______.a. rowb. column10. In a payoff table, probabilities are given for __________.a. decision alternativesb. states of nature

c. Both a and b.

11. In the decision theory, the term decision making under uncertainty refers to __________ .a. the possible risk in a decision.b. the feature of danger in the process of decision making.c. a type of decision making in which probabilities for the states of natures are known.d. a type of decision making in which probabilities for the states of natures are unknown.12. ___________ is the criterion for making the decision in decision making under risk.a. Expected monetary value (EMV)b. Expected value of perfect information (EVPI)c. Probabilities of decision alternativesd. Probabilities of states of nature13. Which is the correct interpretation of EMV?a. The EMV is the expected payoff of all decision alternatives under all states of nature.b. An EMV is the expected payoff of a decision alternative.c. An EMV is the expected payoff of a state of nature.

14. What is the correct interpretation of EVPI?

a. EVPI is the dollar amount that is asked by a consulting firm for the perfect information.b. EVPI is the benchmark up to which a decision maker would be willing to pay for additional information..c. EVPI is the expected monetary value of an alternative.d. EVPI is the maximum expected monetary value.15. Which is not a criterion (approach) for decision making under risk?a. Max EMVb. Min EOLc. EVPI16. What is not a criterion for decision making under uncertainty?a. Max EMVb. MaxiMaxc. MaxiMind. Max Hurwicz valuee. Equally likely f. MiniMax Regret17. Which criterion is for a very conservative risk-averter ?a. MaxiMaxb. MaxiMin18. If a decision maker is kind of optimistic and loving taking risk, then he would set the coefficient of realism, ,________ when he is using the Hurwicz approach.a. smallerb. larger19. The five criteria (methods), maximax, maximin, minimax regret, Hurwicz, and equal likelihood, are fora. decision making under risk.b. decision making under uncertainty.20. Expected payoff (EMV) is the criterion used ina. decision making under risk.b. decision making under uncertainty.21. The opportunity cost (regret, or opportunity loss) is what you may have earned but you gave it up.a. Trueb. False22. Which of the following approaches needs to develop a regret table in order to make a decision?a. Hurwicazb. Max EMVc. Min EOL23. Suppose the payoffs of three alternatives in state of nature Y are: 300 for Alt.A, 700 for Alt.B, 500 for Alt.C.What is the opportunity loss (opportunity cost) if Alt.A is selected and state of nature turns out to be Y?a. 300b. 400c. 700d. 200e. 400 if selected B and 200 if selected C24. The five criteria (methods), maximax, maximin, minimax regret, Hurwicz, and equal likelihood, always selectthe same alternative as the decision.a. Trueb. False25 We have learned two decision making approaches for decision making under risk: Max EMV and Min EOL. Thetwo approaches always select the same alternative as the best decision.a. Trueb. False26 In a case of decision making under risk, the value of the minimum EOL is always the same as ___________.a. Max EMVb. EVPIc. EVwPId. EVw/oPI27. EVPI = EVwPI EVw/oPI.a. True

b. False

28. EVw/oPI = Max EMV.

a. True

b. False

29 EVwPI = expected value of column maximums in the payoff table.

a. Trueb. False30 In a case of decision making where the probabilities of states of nature are not given, which of the followingdecision approaches can be used?a. MiniMax regretb. Min EOLc. Either a or b.31. If =1 in the Hurwicz method, then it is equivalent to the __________ method.a. Maximaxb. Maximinc. Equal likelihood.d. None of above.32. If =0.5 in the Hurwicz method, then it is equivalent to __________ method.a. Maximaxb. Maximinc. Equal likelihoodd. None of above.33. If =0 in the Hurwicz method, then it is equivalent to __________ method.a. Maximaxb. Maximinc. Equal likelihoodd. None of above.34. Suppose EVPI=$2,000. Is it cost-effective to hire a consultant at $2,200 to do research and provide betterinformation about the states of nature?a. Yesb. No35. Suppose EVPI=$2,000. Is it cost-effective to hire a consultant at $1,990 to do research and provide betterinformation about the states of nature (Do not expect the consultant would provide you with perfect information).a. Yesb. No36. Kay White is considering whether to put $5,000 to the stock market that can be good or bad in the coming year.In the example, states of nature are _________________.a. investing the $5,000 to the stock market, or not.b. good stock market, or bad stock market, in the coming year.For question 37 39:Ben is a manager of a grocery store. He is to decide how many cases of milk should be stocked everythree days. Of course, he wants to sell as many as possible. But if he stock too much, he has to dump the un-soldmilk. If he stock too little, he would lose customers and business. According to the past data, the 3-day demand ofmilk can be anywhere between 60 to 70 cases (i.e., 11 possible values: 60, 61, 62, ..., 70).37. What does Ben want to decide?a. How many cases demanded in three days.b. How many cases to stock for the next three days.c. Get all stocked cases of milk sold, or not.38. What are decision alternatives?a. Number of cases of milk sold in the next three days, with 11 choices: 60, 61, 62, ..., 70.b. Number of cases of milk to stock for the next three days, with 11 choices: 60, 61, 62, ..., 70.c. Number of cases of milk demanded in the next three days, with 11 choices: 60, 61, 62, ..., 70.d. Build a large plant, a small plant, and doing nothing.39. What are the states of nature?a. Get the stocked milk sold or unsold, with two possibilities: Sold and unsold.b. Good market, Fair market, and poor market.c Number of cases of milk sold in the next three days, with 11 choices: 60, 61, 62, ..., 70.d. Number of cases of milk to stock for the next three days, with 11 choices: 60, 61, 62, ..., 70.

e. Number of cases of milk demanded in the next three days, with 11 choices: 60, 61, 62, ..., 70.For Question 40 42, use the following payoff data:State-of-nature 1State-of-nature 2Alternative X8020

State-of-nature 335

40. What is the Hurwicz value for alternative X with =0.3?

a. 38b. 62c. 80

d. 48.5

e. 30

41. What is the Hurwicz value for alternative X with =0.5?

a. 35b. 50c. 45

d. 57.5

e. 80

42. What is the average payoff of alternative X in the criterion of "equal likelihood"?a. 35b. 50c. 45d. 20e. 80For questions 43 47, use the information in this payoff table :States of NatureAAlternativesP(A)=0.21$3,0002$1,5003$2,500

BP(B)=0.8$1,000$2,000$3,500

43. If you chose Alternative 2, then the expected monetary value (EMV) would be $____________.44. If you chose Alternative 2 and the state of nature turned out to be B, then the opportunity loss (regret) would be$___________.45. The best payoff under the state of nature of B is $____________?46. Which alternative would you select if perfect information (PI) said that the state of nature would be A ?a. Alternative 1b. Alternative 2c. Alternative 347. Calculate the expected value with perfect information, EVwPI.

48. EVPI is the value of information from _____________ standpoint of view.

a. information generatorsb. information users49. Suppose Company X is negotiating with a consulting firm C on purchasing information about prediction ofeconomy development in the next year. In this case, EVPI is a benchmark on the value of information for____________.a. Company Xb. Consulting firm C